Quantification of turbulence and velocity in stenotic flow using spiral three-dimensional phase-contrast MRI

Quantification of turbulence and velocity in

stenotic flow using spiral three-dimensional

phase-contrast MRI

Sven Petersson, Petter Dyverfeldt, Andreas Sigfridsson, Jonas Lantz, Carljohan Carlhäll and

Tino Ebbers

Linköping University Post Print

N.B.: When citing this work, cite the original article.

Original Publication:

Sven Petersson, Petter Dyverfeldt, Andreas Sigfridsson, Jonas Lantz, Carljohan Carlhäll and

Tino Ebbers, Quantification of turbulence and velocity in stenotic flow using spiral

three-dimensional phase-contrast MRI, 2016, Magnetic Resonance in Medicine, (75), 3, 1249-1255.

http://dx.doi.org/10.1002/mrm.25698

Copyright: Wiley

http://eu.wiley.com/WileyCDA/

Postprint available at: Linköping University Electronic Press

METHODOLOGY

-Notes

Quantification of Turbulence and Velocity in Stenotic

Flow Using Spiral Three-Dimensional Phase-Contrast

MRI

Sven Petersson,

* Petter Dyverfeldt,

Andreas Sigfridsson,

Jonas Lantz,

Carl-Johan Carlh€

all,

and Tino Ebbers

Purpose: Evaluate spiral three-dimensional (3D) phase con-trast MRI for the assessment of turbulence and velocity in ste-notic flow.

Methods: A-stack-of-spirals 3D phase contrast MRI sequence was evaluated in vitro against a conventional Cartesian sequence. Measurements were made in a flow phantom with a 75% stenosis. Both spiral and Cartesian imaging were performed using different scan orientations and flow rates. Volume flow rate, maximum velocity and turbulent kinetic energy (TKE) were computed for both methods. Moreover, the estimated TKE was compared with computational fluid dynamics (CFD) data.

Results: There was good agreement between the turbulent kinetic energy from the spiral, Cartesian and CFD data. Flow rate and maximum velocity from the spiral data agreed well with Cartesian data. As expected, the short echo time of the spiral sequence resulted in less prominent displacement artifacts compared with the Cartesian sequence. However, both spiral and Cartesian flow rate estimates were sensitive to displace-ment when the flow was oblique to the encoding directions. Conclusion: Spiral 3D phase contrast MRI appears favorable for the assessment of stenotic flow. The spiral sequence was more than three times faster and less sensitive to displace-ment artifacts when compared with a conventional Cartesian sequence. Magn Reson Med 75:1249–1255, 2016. VC ₂₀₁₅

Wiley Periodicals, Inc.

Key words: phase contrast mri; 4d flow; turbulence mapping; spiral; stenosis

INTRODUCTION

Stenotic flow is often characterized by high-velocity jets, high acceleration, and disturbed or turbulent flow fluctu-ations. These turbulent flow fluctuations drastically decrease the transport efficiency of the blood due to vis-cous dissipation, which is the major cause of pressure drop over a constriction. Exposure of biological tissue to abnormal turbulent stresses can also cause tissue dam-age, such as mechanical damage of blood constituents resulting in hemolysis and compromised hemostasis (1) and endothelial dysfunction (2).

Time-resolved three-dimensional (3D) phase-contrast (PC) MRI, referred to as 4D flow MRI, is a powerful tool for the quantification of a range of hemodynamic param-eters in stenotic flow, such as flow eccentricity, turbu-lent kinetic energy (TKE) and pressure drop (3–7). However, the application of 4D flow MRI is limited by long scan times and many PC-MRI artifacts are more prominent in stenotic flow. High velocities and accelera-tion may result in spatial misregistraaccelera-tion (displacement) artifacts. Furthermore, disturbed and turbulent flow can cause flow-related signal loss due to intravoxel phase dispersion (8), and ghosting due to view-to-view variations. This signal loss can lead to inaccurate flow estimates, but can be decreased by usage of shorter echo times (TE) (8). Ultrashort TE PC-MRI have been shown to reduce artifacts such as signal loss, as well as to increase the accuracy of flow quantification of stenotic flow (9–11), but it does not decrease the long scan times. Spiral readouts starts in the center of k-space, leading to a shorter TE and less T2* signal decay in the center of k-space, which is advantageous in the assessment of ste-notic flow. These trajectories are also very efficient, as a large part of the repetition time (TR) can be spent on actually reading data. In aortic 4D flow MRI, spiral read-outs have been shown to reduce the scan time of aortic 4D flow MRI by a factor of two to three compared with a conventional Cartesian measurement (with a SENSE factor of two), without reducing the data quality for pathline analysis and measurement of cardiac output (12). Spiral trajectories have previously been shown to be suitable for 2D PC-MRI of high-speed flow jets (13) and unsteady flow systems (14). A recent study, evaluated spiral 4D PC-MRI and found that the short TE of spiral trajectories are advantageous when assessing maximum velocity and flow rate in stenotic nonpulsatile flow in vitro (15). However, the effect of

1

Division of Cardiovascular Medicine, Department of Medical and Health Sciences, Link€oping University, Link€oping, Sweden.

2

Center for Medical Image Science and Visualization (CMIV), Link€oping University, Link€oping, Sweden.

3

Division of Media and Information Technology, Department of Science and Technology/Swedish e-Science Research Centre (SeRC), Link€oping Univer-sity, Link€oping, Sweden.

4

Department of Clinical Physiology, Karolinska Institutet and Karolinska University Hospital, Stockholm, Sweden.

5

Department of Clinical Physiology, Institution of Medicine and Health Sciences, Link€oping University, Link€oping, Sweden.

Grant sponsor: This research was funded by the European Research Coun-cil; Grant number: 310612; Grant sponsor: the Swedish Research Council, and the Swedish e-Science Research Centre.

*Correspondence to: Sven Petersson KVM, Ph.D., Department of Medical and Health Sciences, Link€oping University, SE-581 83 Link€oping, Sweden. E-mail: sven.petersson@liu.se

Correction added after online publication 6 October 2015. The author has added a footnote statement to include funding information.

Received 7 November 2014; revised 3 February 2015; accepted 24 February 2015

DOI 10.1002/mrm.25698

Published online 4 April 2015 in Wiley Online Library (wileyonlinelibrary.com).

Magnetic Resonance in Medicine 75:1249–1255 (2016)

spiral sampling on the assessment of TKE has not yet been investigated.

The aim of this work was to evaluate spiral three-directional 3D PC-MRI for the assessment of turbulence and velocity in stenotic flow. A 3D PC-MRI stack-of-spi-rals sequence was evaluated in an in vitro flow phantom against a conventional Cartesian sequence and computa-tional fluid dynamics (CFD) data. The assessment of TKE, volume flow rate, maximum velocity, and the effect of displacement artifacts were compared between Carte-sian and spiral acquisition techniques.

METHODS

Both spiral and Cartesian imaging were performed using three different scan orientations and four different flow rates in an in vitro flow model of stenotic flow, as described below. Numerical flow data resolving the tur-bulent velocities were obtained using CFD simulations. In Vitro Flow Phantom

Measurements of steady flow were made in an in vitro flow phantom consisting of a straight rigid plastic pipe with an inner diameter of 14.6 mm, and a 75% area reduction ste-nosis (16,17). The entrance length was approximately 100 diameters. A gear pump (Gearchem G6, Pulsafeeder, Roch-ester, NY) was connected to the phantom by means of plas-tic hoses. The pump was fed by a computer-controlled AC servo motor (JVL Industri Elektronik A/S, Blokken, Den-mark). A honeycomb flow straightener was placed at the inlet to reduce flow structures. The fluid used was water at 23_{C. Water-filled bottles were placed around the phantom} to improve coil loading.

Measurements were performed at volume flow rate 10 mL/s, 20 mL/s, 56 mL/s, and 112 mL/s, resulting in a jet velocity of approximately 0.3 m/s, 0.6 m/s, 1.4 m/s, and 2.8 m/s, respectively.

Acquisition and Postprocessing

A clinical 1.5 Tesla (T) MRI system (Achieva, Philips, Best, The Netherlands) with 33 mT/m gradient strength and 180 T/m/s slew rate was used for all measurements. The spiral sequence consisted of a stack of spirals, and every slice consisted of 12–15 spiral interleaves. Conven-tional Cartesian scans with identical spatial resolution were used for comparison.

The effect of scan orientation was assessed by using three different orientations: (i) coronal (COR) with fre-quency and spiral encoding in the flow direction, (ii) transverse (TRA) with slice encoding in the flow direc-tion, and (iii) oblique (OBL) orientation with frequency and slice encoding in the flow direction (45_{). As the} viscosity of water is low compared with blood, physio-logical turbulent velocity fluctuations and physiophysio-logical velocities could not be achieved simultaneously. There-fore, at flow rates 10 and 20 mL/s, which correspond to Reynolds numbers 1000 and 2000, respectively, two velocity encoding ranges (VENC) were used: one was optimized for turbulence mapping, and a second higher VENC was optimized for velocity mapping without alias-ing. The low VENCs resulted in longer TE and repetition

time (TR) as the maximum gradient strength was already reached. At flow rates 56 and 112 mL/s, which resulted in maximum velocities corresponding to clinically slightly increased aortic velocity (increased-flow) and mild to moderate aortic stenosis (stenotic-flow), only velocity mapping and assessment of displacement arti-facts were carried out. Scan parameters for all scans are shown in Table 1. Gradient spoiling was used for all sequences in the phase-encoding directions and no RF-spoiling was used. The TE in the spiral velocity meas-urements for the two higher VENCs was 2.1–2.4 ms shorter than the TE for the Cartesian measurements.

For each velocity scan, an identical scan was carried out with the pump turned off. The velocities from these scans were smoothed using a spatial filter and then sub-tracted from the velocity data so as to correct for velocity offsets. A total three to seven signal averages were used to boost SNR.

Numerical Flow Data

Numerical flow data was used to evaluate eventual dis-crepancies between spiral and Cartesian sampling. The flow inside the phantom for Reynolds numbers 1000 and 2000 was simulated numerically by solving the Navier-Stokes equations in ANSYS CFX 14.0. A computational mesh was made in ANSYS ICEM 14.0 and contained 10 million high quality anisotropic hexahedral cells. The nondimensional wall distance Yþ was always less than one to ensure a good near-wall resolution, and the thick-ness of the mesh cells close to the wall grew exponen-tially by a factor of 1.05 until it matched the mesh size in the center of the phantom. Turbulent flow fluctua-tions were resolved using Large Eddy Simulation (LES), a technique that resolves the larger energy-carrying tur-bulent scales and models the smaller isotropic scales where energy dissipation occurs. The simulation used the WALE sub-grid scale model (18), and the numerical schemes were second order accurate. The time step was 5105s, which has been shown to be sufficient for these kinds of flow (18–20), and also gave a Courant number of less than one. The convergence criterion was 1106 and global imbalances of mass and momentum were always less than 0.1. Sampling of flow statistics was started after initial transient effects had disappeared. Results were extracted along the centerline after the results had converged.

Velocity profiles from the MRI measurements were pre-scribed at the inlet of the model as boundary conditions, while the outlet used a constant static pressure. The walls were considered rigid and to obey the no-slip condition. The fluid was water with a constant density of 997 [kg/ m3] and dynamic viscosity of 8.899104[kg m1s1]. Data Analysis

Turbulent kinetic energy can be computed from intra-voxel velocity standard variation (IVSD), which can be obtained from the flow-induced signal loss (16,21,22). Estimates of IVSD from 4D flow MRI with Cartesian sam-pling have been shown to agree well with laser Doppler anemometry measurements, particle image velocimetry, and computer fluid dynamics (CFD) simulations of both

in vitro and in vivo flow (17,20,23,24). The TKE per voxel was computed from the IVSD in the three direc-tions as

TKE ¼r 2ðIVSD

2

Xþ IVSDY2 þ IVSDZ2Þ [1]

where r is the density of water. The total TKE in the post-stenotic region of the phantom was obtained by integrating the TKE in the phantom between the center

of the stenosis (X ¼ 0) and six diameters downstream (X ¼ 6).

The velocities and turbulent kinetic energy were inter-polated along the centerline of the phantom. Maximum velocities were obtained by finding the maximum speed in a segmentation of the phantom. To make the maxi-mum velocity estimates less noise dependent the speed data was first smoothed using a Gaussian kernel, which was five voxels wide (the inner diameter of the phantom is 9.7 voxels wide). The TKE estimates were also eval-uated by computing the root-mean-square error (RMSE) with the Cartesian TRA measurement as reference. As the FOV is slightly different between the two methods and the two orientations, it was necessary to interpolate all data to the Cartesian TRA grid to perform voxel-to-voxel comparison.

The volume flow rates were computed from a segmen-tation of the through-plane velocity at cross-sectional planes of the phantom. An automatic segmentation was based on the true radius of the vessel. This segmentation was then controlled and, if necessary, edited manually to fit the magnitude data. According to the continuity equation, the flow rate should be equal along the phantom.

RESULTS

The estimated maximum velocities were in the interval of 1.37 to 1.46 m/s and 1.34 to 1.39 m/s for the spiral and Cartesian measurements of the increased-flow case, respectively (Table 2). For the stenotic-flow case, the maximum velocities were 2.69 to 2.75 m/s and 2.66 to

Table 2

Maximum Velocity and Total Turbulent Kinetic Energya

Max velocity [m/s] Increased-flow Stenotic-flow

Spiral TRA 1.37 2.70 Cartesian TRA 1.39 2.67 Spiral COR 1.39 2.69 Cartesian COR 1.35 2.66 Spiral OBL 1.46 2.75 Cartesian OBL 1.34 2.87 Total TKE [J] Re. 1000 Re. 2000 Spiral TRA 2.08*105 9.56*105 Cartesian TRA 2.03*105 9.36*105 Spiral COR 1.96*105 8.71*105 Cartesian COR 1.94*105 7.79*105 CFD 1.88*105 6.82*105 a

The VENC was 150 and 300 cm/s for the increased-flow and stenotic-flow cases, respectively. The VENC was 10 and 35 cm/s for Reynolds number 1000 and 2000, respectively. The TKE was integrated between the center of the stenosis and six diameters downstream.

Table 1

MRI Scan Parameters.

Scan VENC [cm/s] Scan time [min] No. of readouts TE [ms] TR [ms] Interleaves  spiral duration [ms] Matrix Voxel size [mm] Flip angle Spiral COR 10 1:36 285 5.9 14.1 155.5 11211215 1.5 9.7 35 1:21 3.7 11.9 70 1:16 3.0 11.2 150 0:49 2.4 10.5 300 0:48 2.1 10.3 Spiral TRA 10 11:40 1224 5.9 14.5 126 969680 1.5 9.7 35 8:44 3.7 12.3 70 5:34 2.9 11.5 150 2:40 2.3 10.9 300 2:34 1.9 10.5 Spiral OBL 150 2:40 1224 2.3 10.9 155.5 969680 1.5 9.7 300 2:34 1.9 10.5 Cart. COR 10 7:31 1634 8.1 11.4 - 11211215 1.5 8.5 35 5:51 5.5 8.9 70 5:29 4.9 8.2 150 3:31 4.5 7.9 300 3:29 4.5 7.8 Cart. TRA 10 22:31 4284 8.2 11.6 - 808080 1.5 8.5 35 18.14 5.7 9.1 70 16:43 4.9 8.3 150 6:48 4.5 7.9 300 6:41 4.3 7.7 Cart. OBL 150 6:48 4284 4.5 7.9 - 808080 1.5 8.5 300 6:41 4.3 7.7

2.87 m/s for the spiral and Cartesian measurements, respectively (Table 2).

The spiral and Cartesian measurements resulted in similar total TKE for both Reynolds numbers, even though the COR orientation resulted in slightly lower estimates compared with TRA for both methods (Table 2). The total TKE from the CFD data was slightly lower than the MRI based estimates. Moreover, the TKE along

the centerline of the phantom matched well between the spiral and Cartesian measurements for all combinations of Reynolds numbers and orientations (Fig. 1b). Overall, the spiral and Cartesian TKE data agreed well with the CFD TKE data. Visual inspection of TKE images also showed good agreement and no apparent discrepancies between the spiral and Cartesian data (Fig. 1c). For Reyn-olds number 1000, the RMSE from the comparison with Cartesian TRA was 0.52 and 0.39 Pa for the spiral and Cartesian COR measurements, respectively. For Reynolds number 2000, the RMSE from the comparison with Car-tesian TRA was 3.21 and 3.26 Pa for the spiral and Carte-sian COR measurements, respectively. For spiral TRA, the RMSE was 0.41 and 3.22 for Reynolds number 1000 and 2000, respectively.

Displacement was smaller for the spiral COR measure-ment compared the Cartesian COR, which was especially apparent at the site of flow acceleration (Fig. 2a). In the spiral and Cartesian OBL measurements, displacement can be seen in magnitude and flow images for both methods, but is less prominent in the spiral measure-ment (Fig. 2b,c). The stenosis is displaced toward the upper left corner of the images.

Flow rate estimates were rather consistent upstream of the stenosis as well as after 4 diameters downstream of the stenosis. However, over the jet, the flow rate esti-mates varied more, especially for the OBL orientations where around 50% higher values were obtained (Fig. 3).

DISCUSSION

Spiral 3D PC-MRI was evaluated for the assessment of stenotic flow in vitro. The TKE velocity, and volume flow rate from the spiral and Cartesian measurements agreed well for all flows. Displacement artifacts were less prominent in the spiral measurements and the scan time of the spiral sequence was 1/3 of the Cartesian sequence.

Maximum velocity estimates from the different orienta-tions and sequences show relatively small differences. In 2D through-plane velocity measurements, the maximum velocity is underestimated if the flow jet is not perpen-dicular to the plane (13). This problem is not expected in our study, as we used a dimensional and three-directional velocity measurement. Instead, we see a slight increase of the measurement of the maximum velocity in the jet for the oblique orientation. Measure-ments with spiral readouts on a similar phantom have shown that a TE longer than 3 ms will result in less accurate maximum velocity estimates (15). In the present work, TE was 1.9–2.5 ms and 4.3–4.5 ms for the spiral and Cartesian maximum velocity measurements, respectively.

The flow rate estimates from the spiral and Cartesian measurements agreed well. However, the flow rate esti-mates seem to be less accurate when the estimation is performed in the region of the post-stenotic flow jet, especially for the OBL orientations. This corresponds well to previous observations of flow rate measured with 4D flow spiral measurements in jet regions (15). For 2D through-plane PC-MRI, a TE longer than 3 ms has been shown to cause severe underestimation of flow rate for

FIG. 1. The velocity (a) and turbulent kinetic energy (b) along the centerline of the phantom together with cross-sectional images (c) of the turbulent kinetic energy for Reynolds number 1000 (left) and 2000 (right) from Spiral and Cartesian 3D PC-MRI, for two differ-ent oridiffer-entations, coronal (COR) and transverse (TRA), as well as CFD data. The VENC was 35 and 10 cm/s for the velocity and tur-bulence mapping, respectively. X and Y denote distance from the center of the stenosis normalized by the unconstructed pipe diameter (14.6 mm). The principal flow direction is in the positive X-direction.

actual flow rates over 300 mL/s (8). Moreover, the peak flow rate in pulsatile stenotic flow was shown to be underestimated using a 4D flow sequence with a TE of 3.9 ms for peak flow rates over 250 mL/s, while for an ultrashort TE sequence with a TE of around 1 ms no

underestimation was seen (11). No apparent underesti-mation was observed in this work for flows up to 112 mL/s. Flow rate estimates from the spiral measure-ments may be influenced by misregistration of low and high frequencies for moving objects, which can occur when the low frequencies (center of k-space) are acquired before the high (25,26). However, this misregis-tration would be most prominent for regions represented by high frequencies in k-space, and those regions mainly exist at physical boundaries of the flow, which are char-acterized by low velocities (14). Also, the short spiral readouts used in this work reduce this misregistration effect. The spiral readouts also result in a time-varying first gradient moment, which causes the velocity encod-ing to vary across k-space. This effect increases toward the periphery of k-space and results in a broadened point-spread function for moving objects (26,27). The flow jet is surrounded by back flow, potentially resulting in partial volume artifacts in the boundary between the jet and the backflow, and this may have contributed to the decreased accuracy in the flow-rate estimates.

There was good overall agreement between the TKE from CFD and the two different MRI methods. However, the simulated CFD data deviated slightly from the meas-ured flow, likely due to the sensitivity of inlet conditions in the simulation of turbulent flow. Small changes of the inlet conditions may have a large influence on the result-ing data. No apparent differences between the spiral and Cartesian TKE estimates were found. The total TKE from the spiral and Cartesian measurements agreed well, although there were some discrepancies between the COR and TRA orientations. The total TKE in the post-stenotic region from the CFD data was lower than the total TKE estimated from the MRI measurements. Addi-tional contributions from noise and shear stresses in the IVSD estimation as well as deviations between simulated and measured flow may have contributed to the differ-ence in total TKE. The TKE contribution in the MRI data from the shear stresses surrounding the jet is seen most clearly for Reynolds number 2000 (Fig. 1c), while no ele-vated TKE values in this region are seen in the CFD data. The RMSE values with Cartesian TRA as reference were around 10% of the maximum TKE. For Reynolds number 1000, spiral COR performed slightly less good than Cartesian COR, but this difference was not seen for Reynolds number 2000. Errors in interpolation between the different grids may have resulted in higher RMSE.

FIG. 2. a: Plots of the velocity along the centerline of the phantom of the increased-flow case (left) and stenotic-flow case (right), respectively. Both Cartesian and spiral velocity data from the cor-onal (COR) and transverse (TRA) orientations are shown. The prin-cipal flow direction is in the positive X-direction. Images of magnitude (b) and speed (c) from the oblique (OBL) orientation of the increased-flow case (left) and stenotic-flow case (right). The VENC was 150 and 300 cm/s for the increased-flow case and stenotic-flow case, respectively. X denotes the distance from the center of the stenosis normalized by the unconstructed pipe diameter (14.6 mm). For the OBL orientation, frequency and slice encoding was carried out along the vertical and horizontal axis, respectively.

The TE of the spiral measurements was approximately half the TE of the Cartesian measurements. This may be expected to result in around a 50% decrease in spatial misregistration. In the present study, displacement arti-facts were, in general, less pronounced in the spiral com-pared with the Cartesian measurements. However, in the oblique measurements, both the Cartesian and spiral measurements performed poorly in terms of volumetric flow-rate estimation in the region of the jet. In the oblique measurements, the displacement will cause the signal from spins with high velocities to move toward the edge of the phantom; however, there stills seems to be some remaining signal with high velocities in the cen-ter, resulting in a wider jet, and consequently an overes-timation of the flow rate. The TE in the spiral measurements might not have been short enough to avoid these effects completely. Postprocessing techni-ques might be used to reduce the effects of velocity dis-placement (28).

The scan time of the COR spiral scans was only 23% of the time of the corresponding Cartesian scans. For the TRA scans, the spiral scan time was 39% of the Carte-sian scan, which had a slightly smaller field of view. Parallel imaging or longer spiral readouts would further decrease the scan time of spiral 4D flow MRI. Here, the length of the spiral readouts was kept short to obtain a reasonable temporal resolution in an in vivo scan. No off-resonance correction was deemed necessary, as the spiral readouts were relatively short (12). Alternative spi-ral readouts, such as spherical stack of spispi-rals, spispi-ral shells, and spiral cones (27) could also further reduce the scan time and have the same benefits of a short TE. While the behavior of a spherical stack of spirals should be similar to the sequence used in this work, more com-plex 3D readouts may be more sensitive to flow (27) and require longer readouts, which increase the sensitivity to off-resonance and inhomogeneity. Moreover, a stack of spirals approach allow for a nonisotropic field of view and resolution.

A limitation of this study was that only steady flow was imaged, while in vivo flow is pulsatile. Pulsatile

flow may induce more artifacts, as there will be accelera-tion in both the spatial and temporal domain. Signal-to-noise ratio (SNR) of the spiral sequence was not eval-uated in this study, but previous studies indicate that a spiral sequence has similar SNR to a Cartesian scan accelerated using SENSE factor 2, but is twice as fast (12). Furthermore, the SNR was boosted using signal averaging to better depict the effects of displacement. While no obvious susceptibility artifacts were observed, this may be a problem for longer spiral readouts or higher field strengths, especially if the vessel, or phan-tom in this case, is surrounded by air. Moreover, partial volume artifacts are not faithfully reproduced using this phantom, as the plastic wall give no signal. The lack of surrounding tissue outside the phantom may also have degraded the flow rate estimates, as it increases the risk of including noise in the segmentation.

To acquire accurate turbulence estimates, a VENC that is too low to avoid velocity aliasing in a stenotic jet was necessary (23). This problem is less prone in in vivo, as the viscosity of blood is higher, resulting in lower Reyn-olds numbers, and less intense turbulent velocity fluctu-ations for the same flow rate. By using a 5-point dual VENC approach (29,30), these aliasing artifacts can be avoided. Furthermore, multipoint PC-MRI and Bayesian analysis have been used to increase the accuracy and dynamic range of turbulence estimates (31).

CONCLUSIONS

Spiral three-directional 3D PC-MRI appears favorable for the assessment of stenotic flow. The spiral sequence was three times faster, and less sensitive to displace-ment artifacts, when compared with a conventional Car-tesian sequence. However, flow-rate estimates in the jet from both methods seem to be sensitive to displacement in some directions. Turbulent kinetic energy obtained with spiral 3D PC-MRI agreed well with Cartesian data and CFD. Moreover, maximum velocity and volume flow rate values from the spiral and Cartesian data agreed well.

FIG. 3. The volume flow rate from the increased-flow case (a) and the stenotic-flow case (b) for the different orientations. The VENC was 150 and 300 cm/s for these two flow cases, respectively. X denotes position of the cross sectional plane from which the flow rate was computed and is the distance from the center of the stenosis normalized by the unconstructed pipe diameter (14.6 mm). The prin-cipal flow direction is in the positive X-direction. Nominal flow rate should be 56 mL/s in the increased-flow case and 112 mL/s in the stenotic-flow case, for all planes.

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